AMC8 2013

AMC8 2013 · Q19

AMC8 2013 · Q19. It mainly tests Logic puzzles.

Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don't show their tests to anyone. Cassie says, "I didn't get the lowest score in our class," and Bridget adds, "I didn't get the highest score." What is the ranking of the three girls from highest to lowest?

布里奇特、卡西和汉娜在讨论她们上次数学考试的结果。汉娜向布里奇特和卡西展示了她的试卷，但布里奇特和卡西没有向任何人展示她们的试卷。卡西说：“我没有得到班上最低的分数。”布里奇特补充说：“我没有得到最高的分数。”这三个女孩从最高到最低的排名是什么？

(A) Hannah, Cassie, Bridget Hannah, Cassie, Bridget

(B) Hannah, Bridget, Cassie Hannah, Bridget, Cassie

(D) Cassie, Hannah, Bridget Cassie, Hannah, Bridget

(E) Bridget, Cassie, Hannah Bridget, Cassie, Hannah

Answer

Correct choice: (D)

正确答案：（D）

Solution

If Hannah did better than Cassie, there would be no way she could know for sure that she didn't get the lowest score in the class. Therefore, Hannah did worse than Cassie. Similarly, if Hannah did worse than Bridget, there is no way Bridget could have known that she didn't get the highest in the class. Therefore, Hannah did better than Bridget, so our order is $\boxed{\textbf{(D) Cassie, Hannah, Bridget}}$ Note: It could be said that Cassie did better than Hannah, and Bridget knew this, and she had the same score as Hannah, so Bridget didn't get the highest score. This may be a reason that MAA didn't put this answer choice in.

如果汉娜比卡西考得好，她就没有办法确信自己没有得到班上最低分。因此，汉娜比卡西考得差。同样，如果汉娜比布里奇特考得差，布里奇特就没有办法知道自己没有得到班上最高分。因此，汉娜比布里奇特考得好，所以顺序是 $\boxed{\textbf{(D) Cassie, Hannah, Bridget}}$ 注意：可以说卡西比汉娜考得好，布里奇特知道这一点，并且她和汉娜分数相同，所以布里奇特没有得到最高分。这可能是 MAA 没有把这个答案选项放进去的原因。

Topics

LM.001 Logic puzzles